I think you are incorrect with regards to Hume's is-ought gap, although I find its relevance to be somewhat overstated. A hypothetical imperative such as your example relies on an equivocation between 'ought' as (1) a normative injunction and (2) conveying a possible causal pathway from here to there.

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Here is the incorrect syllogism:

Premise 1: A desires C (is)

Premise 2: B will produce C (is)

Conclusion: A ought to do B (ought)

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There is a hidden normative premise that is often ignored. It is

Premise 3: A should obtain its desires. (ought)

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The correct syllogism would then be:

Premise 1 (is): A desires C

Premise 2 (is): B will produce C

Premise 3 (ought): A ought to obtain its desires.

Conclusion: A ought to do B (ought)

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The necessity of Premise 3 is made clear by use of an admittedly extreme example:

P1: Hitler wants to kill a great number of people

P2: Zyklon B will kill a great number of people

C1: Hitler ought to use Zyklon B to kill a great number of people

While the conclusion is derived from the premises using definition (2) of the word 'ought', few would express it as a normative recommendation.

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Hume's fact/value dichotomy remains valid. A normative conclusion can only be validly deduced from a group of premises including at least one which is itself normative.